A suicide attacker detonated a car bomb in west Baghdad killing 11 people, some of whom were about to apply to join the Iraqi security forces.
The first car bomb hit a busy commercial and residential area
Hours later another blast shook the Mansour district of Baghdad.
No deaths are reported, but at least three people were hurt and two US military vehicles were destroyed.
The Iraqi capital has seen almost daily bombings in the past two weeks against US forces and their allies, but most of the victims have been civilians.
Meanwhile, fighting raged in north-east Baghdad after US forces launched a major operation against militants loyal to radical cleric Moqtada Sadr.
At least 15 people are reported to have died in the clashes in the Sadr City suburb.
In other developments:
- A US soldier died in an attack on a patrol in the northern city of Mosul.
- A US Army soldier died when a roadside bomb he was investigating in Tikrit detonated.
- Three US soldiers were injured when their Blackhawk helicopter
made emergency landing late near Nasiriya.
Witnesses in western Baghdad's Jamiyah neighbourhood said it was not immediately clear why the suicide bomber struck in their area, a commercial and residential district.
"I don't even know who they were targeting. They just bombed people eating ice cream" said one casualty who had shrapnel wounds to the face and neck.
However, later reports said a photocopying shop may have been the target, where young men had been preparing their applications before volunteering at a nearby recruitment centre.
At least 13 vehicles were wrecked by the blast and the engine of the explosives-laden car was hurled about 50 meters (150 feet).
The death toll has been steadily rising during the morning in the restive Shia slum of Sadr City.
Witnesses said US forces used attack helicopters and C130 gun ships to rake some areas with fire.
One US helicopter was reportedly hit by gunfire, but managed to return to its base, and a tank was reported hit by a roadside bomb.
Reports say that, at one point, US troops took to the rooftops in pursuit of five armed militiamen, killing two and capturing three.
"We are fighting the terrorists so we can re-establish civil-military operations and get back to the reconstruction projects that the people of Sadr City want," a US army spokesman said.